Morin, Pascal and Murray, Richard M. and Praly, L. (1997) Nonlinear Rescaling of Control Laws with Application to Stabilization in the Presence of Magnitude Saturation. California Institute of Technology , Pasadena, CA. (Submitted) http://resolver.caltech.edu/CaltechCDSTR:1997.014
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Motivated by some recent results on the stabilization of homogeneous systems, we present a gain-scheduling approach for the stabilization of non-linear systems. Given a one-parameter family of stabilizing feedbacks and associated Lyapunov functions, we show how the parameter can be rescaled as a function of the state to give a new stabilizing controller. In the case of homogeneous systems, we obtain generalizations of some existing results. We show that this approach can also be applied to nonhomogeneous systems. In particular, the main application considered in this paper is to the problem of stabilization with magnitude limitations. For this problem, we develop a design method for single-input controllable systems with eigenvalues in the left closed plane.
|Item Type:||Report or Paper (Technical Report)|
|Additional Information:||P. Morin contributed to this work while he was with the CDS Dept. at Caltech as a Post-doctoral fellow.|
|Group:||Control and Dynamical Systems Technical Reports|
|Subject Keywords:||gain scheduling, global stabilization, bounded control, nonlinear feedback|
|Official Citation:||Morin, Pascal, Murray, Richard M. and Praly, L. (1997) Nonlinear Rescaling of Control Laws with Application to Stabilization in the Presence of Magnitude Saturation. Technical Report. California Institute of Technology, Pasadena, CA. [http://resolved.caltech.edu/CaltechCDSTR:1997.014]|
|Usage Policy:||You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.|
|Deposited By:||Imported from CaltechCDSTR|
|Deposited On:||19 Dec 2007|
|Last Modified:||26 Dec 2012 14:31|
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